# Properties

 Label 5070.2.b Level $5070$ Weight $2$ Character orbit 5070.b Rep. character $\chi_{5070}(1351,\cdot)$ Character field $\Q$ Dimension $100$ Newform subspaces $27$ Sturm bound $2184$ Trace bound $22$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5070.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$27$$ Sturm bound: $$2184$$ Trace bound: $$22$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$, $$31$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(5070, [\chi])$$.

Total New Old
Modular forms 1148 100 1048
Cusp forms 1036 100 936
Eisenstein series 112 0 112

## Trace form

 $$100 q + 4 q^{3} - 100 q^{4} + 100 q^{9} + O(q^{10})$$ $$100 q + 4 q^{3} - 100 q^{4} + 100 q^{9} - 4 q^{10} - 4 q^{12} - 8 q^{14} + 100 q^{16} - 8 q^{22} - 100 q^{25} + 4 q^{27} - 16 q^{29} - 4 q^{30} - 8 q^{35} - 100 q^{36} + 32 q^{38} + 4 q^{40} + 8 q^{42} - 16 q^{43} + 4 q^{48} - 52 q^{49} - 8 q^{55} + 8 q^{56} - 40 q^{61} + 16 q^{62} - 100 q^{64} - 8 q^{66} + 16 q^{69} - 8 q^{74} - 4 q^{75} + 80 q^{77} - 16 q^{79} + 100 q^{81} - 16 q^{87} + 8 q^{88} - 4 q^{90} - 32 q^{94} - 32 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(5070, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5070.2.b.a $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+3iq^{7}+\cdots$$
5070.2.b.b $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+3iq^{7}+\cdots$$
5070.2.b.c $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots$$
5070.2.b.d $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots$$
5070.2.b.e $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots$$
5070.2.b.f $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots$$
5070.2.b.g $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots$$
5070.2.b.h $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots$$
5070.2.b.i $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+4iq^{7}+\cdots$$
5070.2.b.j $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots$$
5070.2.b.k $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+4iq^{7}+\cdots$$
5070.2.b.l $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+5iq^{7}+\cdots$$
5070.2.b.m $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}+2iq^{7}+\cdots$$
5070.2.b.n $2$ $40.484$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-iq^{2}+q^{3}-q^{4}+iq^{5}-iq^{6}+2iq^{7}+\cdots$$
5070.2.b.o $4$ $40.484$ $$\Q(\zeta_{12})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}-\zeta_{12}q^{6}+\cdots$$
5070.2.b.p $4$ $40.484$ $$\Q(\zeta_{12})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}+\zeta_{12}q^{6}+\cdots$$
5070.2.b.q $4$ $40.484$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+q^{3}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}q^{6}+\cdots$$
5070.2.b.r $4$ $40.484$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots$$
5070.2.b.s $6$ $40.484$ 6.0.153664.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots$$
5070.2.b.t $6$ $40.484$ 6.0.153664.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots$$
5070.2.b.u $6$ $40.484$ 6.0.153664.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots$$
5070.2.b.v $6$ $40.484$ 6.0.153664.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots$$
5070.2.b.w $6$ $40.484$ 6.0.153664.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots$$
5070.2.b.x $6$ $40.484$ 6.0.153664.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots$$
5070.2.b.y $6$ $40.484$ 6.0.153664.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots$$
5070.2.b.z $6$ $40.484$ 6.0.153664.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots$$
5070.2.b.ba $8$ $40.484$ 8.0.$$\cdots$$.1 None $$0$$ $$8$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(5070, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(5070, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(845, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1690, [\chi])$$$$^{\oplus 2}$$